Power (statistics)

In frequentist statistics, power is a measure of the ability of an experimental design and hypothesis testing setup to detect a particular effect if it is truly present. In typical use, it is a function of the test used (including the desired level of statistical significance), the assumed distribution of the test (for example, the degree of variability, and sample size), and the effect size of interest. High statistical power is related to low variability, large sample sizes, large effects being looked for, and less stringent requirements for statistical significance.

More formally, in the case of a simple hypothesis test with two hypotheses, the power of the test is the probability that the test correctly rejects the null hypothesis (${\displaystyle H_{0}}$) when the alternative hypothesis (${\displaystyle H_{1}}$) is true. It is commonly denoted by ${\displaystyle 1-\beta }$, where ${\displaystyle \beta }$ is the probability of making a type II error (a false negative) if there is a true effect or association.